System Identification Tool

Version 1.6.1 (R9.3b), last mod. 25-Feb-2008 12:34:15

General Notes

The system identification tool (SIT) for MATLAB®
contains the nonlinear extension of the Kalman filter (unscented
Kalman filter). It is a collection of
M-files implementing several numerical schemes (state estimation,
simultaneous state and parameter estimation) within
the framework of state space filtering. Furthermore, a graphical user interface is
provided. It includes a comfortable editing environment
for the design of the models to be fitted.

Requires Matlab 5.3 or higher.

Usage and Notation

State space models considered here are restricted to the continuous-discrete form:

d

—

dt

x

(t)

=

f(x, p, ε),

y(kΔt)

=

h(x(kΔt)) + η(kΔt),

where

y

- observation vector (i.e. multivariate data point),

x

- state vector,

p

- parameter vector,

η

- observational noise (vector),

ε

- dynamical noise (vector),

kΔt

- discrete sampling time (k=0,1,...),

Δt

- sampling rate.

(Currently, the case of dynamical noise is not implemented yet.)

sit calls the main programme for the
system identification. First a data set has to be
imported from a file or generated by using a predefined model.
Afterwards a model can be fitted. Model quations can be
applied within a comfortable euqation editor.
Calling the sitdemo
gives an imagination of the procedure of system identification.

The input notation for the equation editor corresponds to the Matlab syntax

y(1), y(2), ...

- components of the observation vector,

x(1), x(2), ...

- components of the state vector,

p(1), p(2), ...

- components of the parameter vector,

\eta(1), \eta(2), ...

- components of the observational noise,

\epsilon(1), \epsilon(2), ...

- components of the dynamical noise.

This tool stores the applied data in a native format which
is based on a structure array and stored in the Matlab format (MAT).
For more information call help sit.

Data stored in another format as MAT or plain ASCII can also
be imported.

Estimation results are stored as a MAT-file in the
results folder with a sub-prefix _filter or _filter_state
and the current time of estimation. It contains a
structure L, whose fields contain the data and the
parameters of the model system and the estimation. The
estimated states and the estimated parameters are in the
field XEST.

Sessions and models can be saved and loaded. The extension of
these files is EQU. Furthermore, the model equations can be
exported to an M-file in order to use the model with
standard Matlab ODE solvers. Models given by ODE M-files can
be imported into the SIT equation editor, too.

Demos and Examplary Data Set

sitdemo or sitdemo lorenz
calls a demo using the Lorenz
system with two observations.

sitdemo circuit calls a demo where the fitting of a model
to experimental data taken from a circuit in chaotic regime
ist shown. As data the circuit.dat is used and
for the model this that is contained in the
circuit.equ session.

lorenz.equ

A session file for the System Identification Tool (SIT).
It contains a model of the Lorenz system with two
observations and observational noise.

duffing.equ

A session file for the System Identification Tool (SIT).
It contains a model of the Duffing system with one
observation and observational noise.

circuit.equ

A session file for the System Identification Tool (SIT).
It contains a model of 3 states, 9 parameters and
observational noise, which can be fitted to experimental
data of an electric circuit in chaotic regime, which
is given by the file circuit.dat.
The model fitted here is due to Timmer et al., 2000.

circuit.dat

This data set contains potential measurements of an
electrical circuit in chaotic regime. The data are
provided by the benchmark of the predictability contest;
technical details may be found at
y2k.maths.ox.ac.uk/systems/egb.html.

Please respect the copyrights! The content is protected
by the Creative
Commons License. If you use the provided programmes, text or figures,
you have to refer to the given publications and this web site
(tocsy.pik-potsdam.de)
as well.